In this paper the influence of core parameters in Frequency Response Analysis is analyzed through the equivalent circuit impedance matrix of the transformer winding; the parameters of the circuit have been computed using the Finite Element Method. In order to appreciate the behavior of the iron core in comparison to the air core, the frequency dependence of resonances is calculated to show how the air core only influences the results at low frequencies. The core is modeled using a complex permeability, and the parameters of conductivity and permeability are varied to show their influence in the resonances, which turned out to be negligible. In order to explain this behavior, the eigenvalues of the inverse impedance matrix are calculated showing that they are similar for different values of conductivity and permeability. Finally, the magnetic flux i nside and outside the core and its i nfluence in the frequency response is studied.

n this Thesis we study the emergence and evolution of magnetic structures (flux tubes), that are the basic components of active regions, into the solar atmosphere. The coronal dynamics of these flux tubes lies at the origin of violent energy release phenomena, such as solar flares and coronal mass ejections. Only twisted flux tubes survive the crossing of the convective zone and emerge through the photosphere. The flux tube twist preserves the sign with which it was created in the tachocline. The presence of twist in the tube is seen at the photospheric level as an elongation of the polarities, which we call magnetic tongues. This elongation is due to the contribution of the flux tube azimuthal field component to the line-of-sight magnetic field. The spatial distribution of these elongations is related to the active region magnetic helicity sign, while their extensions indicate the degree of torsion in the tube. Therefore, the identification of magnetic tongues is a useful tool to determine the helicity sign of a magnetic configuration, based only in observations. The helicity sign given by the tongues has been verified by comparing it with that determine by other features in 40 active regions. As a contribution to the understanding of the coronal dynamics, we have modeled the magnetic field of a complex active region. We have calculated its topology finding that it is determined by the presence of the coronal magnetic null point. The observations of three homologous flares, that occurred along 29 hours, suggest that they originated by magnetic field reconnection in the null point neighborhood. This reconnection process is forced by continuous flux emergence. Finally, we have computed the magnetic helicity variation due to an ejective event, and we have compared this value to the helicity content in the associated interplanetary magnetic cloud. We have found that both values were in good agreement, indicating that magnetic helicity is a well preserved quantity even under no ideal conditions. These quantitative comparisons, as the more qualitative ones using tongues, are useful tools to find the solar source of an interplanetary event.

The interplanetary medium is filled with a low density plasma that flows from the Sun and is called the solar wind. This wind transports the magnetic structures that are ejected from the solar corona (e.g. coronal mass ejections, CMEs). In this Thesis, we study from a theoretical and observational point of view some aspects of the evolution of CMEs in the interplanetary medium; in particular, of a subset called magnetic clouds (MCs). We model the dynamical evolution of several events that occurred between 1997 and 2004, we quantify their expansion and we compute, using models developed as part of this Thesis, the global invariant quantities (flux and magnetic helicity) that are relevant to a combined analysis of solar events and their interplanetary counterparts. The models we develop are based in a magnetohydrodynamic description of the plasma. We propose a self similar evolution for the cloud structures with different expansion rates in each of their main directions (radial and axial). We start considering only a radial expansion and we proceed to include an axial expansion. Finally, we broaden the description towards a more general formalism, based on observations, that is derived in a hierarchical order and can be applied to more general structures. We show the robustness of global invariants when computed using different expansion models. We quantify for the first time the typical amount of energy lost per unit time in the evolution of a MC. For some of the studied MCs we also analyze observations of the associated solar event and of its source active region. We identify the characteristics of the eruptive regions that allow us to quantify the global invariants in the Sun. We quantify the magnetic flux involved in the ejection and the magnetic helicity variation of the source active region. Finally, we study the evolution of a particular MC from its observation close to Earth until farther than 5 astronomical units using data from two spacecraft aligned with the Sun. We quantify the global invariants in both observational points. We compare these quantities and we provide an interpretation for the origin of the magnetic structure distorted because of its interaction with the solar wind far from the Sun. We extend this comparison to the Sun and we identify the solar source, in this way we achieve a complete description of the MC evolution along the heliosphere.

In this PHD Thesis we study a class of transient phenomena in the solar wind, the so called magnetic clouds (MCs). These events are ejected from the Sun and are composed by plasma, which is cooler than the one in the stationary solar wind. They contain intense magnetic field which is formed by magnetic flux tubes twisted around a main axis; in this way they contain an important amount of magnetic Flux (F ) and magnetic Helicity (H) that are transported from their solar sources through their journey along the heliosphere. We develope a theoretical description of MCs in the frame of magnetohydrodynamic. We revise and develop several methods and techniques for the study of MCs, which allow us to determine MCs properties from the analysis of magnetic and plasma ’in situ’ observations made by spacecraft. We study three samples of events: (a) in the inner heliosphere (from 0.3 to 1 astronomical units), (b) at one astronomical unit, and (c) in the outer heliosphere (from 1.5 to 5 astronomical units). We characterize properties of their magnetic structure and of their dynamical evolution. Results from models are used to quantify F and H in MCs, and we find typical values: F ∼ 1020 − 1021 Mx and H ∼ 1041 − 1042 Mx2 . We find that the impact parameter (minimum distance approach between the cloud axis and the spacecraft) is one of the more critical parameters for making correct modelization of MCs, and we find a method to significantly improve its estimation. We introduce and study a dimensionless expansion coefficient, that allow us to quantify the evolution of the size of MCs in function of the distance to the Sun, and then can be obtained from the in situ observed velocity profile for a given event. We find that MCs can be classified in two sub-classes, those which are significantly perturbed by the solar wind environment, and those which follow a natural evolution, given by the decay of the ambien solar wind pressure.

We study the long-term evolution of bipolar active regions in which the main polarities are observed to rotate one about the other along several solar rotations. We propose that this peculiar evolution is due to the emergence of distorted magnetic flux tubes. We are able to infer the sign of the writhe helicity of the flux tubes from the rotation of the axis joining the main positive and negative polarities. The origin of the deformations may be explained by the development of a kink instability. Another possibility is the interaction with plasma motions during the ascent of the flux tubes in the Convective Zone. We discuss the role of the Coriolis force, convective turbulence and other large-scale motions in this process.

It is widely admitted that the magnetic field plays a fundamental role in the physics of the Sun and other astrophysical objects, confining the plasma an storing huge amounts of energy that is released in the so called catastrophic events. Solar flares give us the best opportunity to understand how the magnetic field acts during such events. The comparision between observations of these impulsive phenomena, and modeling the magnetic field of the active region is a central topic. This leads us to analyze different manifestations of flare activity using simultaneous observations in a wide range of the electromagnetic spectrum as x-rays, UV (ultraviolet), and different spectral lines in the visible, as well as vector magnetograms. To understand the conditions that lead to flare activity in a given active region, we have considered in this Thesis the modeling of its magnetic field, analyzing afterwards the relationship between its topology and the radiative emissions in different spectral regions. A conventional view of magnetic reconnection is mainly based on dhe two dimensional (2-D) picture of an x-type neutral point, or on its extension to 3-D, and it is thought to be accompanied by flux transport across separatrices (places where the field-line mapping is discontinuous). This view is too restrictive when we realize a variety of solar magnetic configurations that have been seen flaring. We have designed an algorithm, called Source Method (Método de Fuentes, MF), to determine the magnetic topology of Active Regions (ARs). The observed photospheric field was extrapolated to the corona using subphotospheric sources, and the topology was defined by the link between these sources. Hα, UV and X-ray flare brightenings were found to be located at the intersection with the chromosphere of the separatrices previously defined. These results and the knowledge we adquired on the properties of magnetic field-line linkage, led us to generalize the concept of separatrices to "quasi-separatrix layers" (quasi-separatrices, CS), and to design a new method (Método de las Cuasi-Separatrices, MCS) to determine the magnetic topology of ARs. CS are regions where the magnetic field-line linkage changes drastically (and discontinuously when the field-lines behave like separatrices). The MCS can be applied to ARs when the photospheric fields has been extrapolated using any kind of technique. We have applied the MCS to observed flaring regions presenting very different magnetic configurations. We have found that the locations of flare brightenings are related to the properties of the field-line linkage of the underlying magnetic region, as expected from the recent development in 3-D magnetic reconnection. The extrapolated coronal field lines representing the structures involved in the analyzed events have their photosperic footpoints located at both sides of the CS. Our results strongly support the idea that magnetic reconnection is at work in this coronal phenomena.

The time evolution of current sheets under the influence of driven stagnation point flows is studied. It is shown that significant physical processes occur during the formation of the current sheet, originated from a sparse magnetic seed field or from an external continuous injection of magnetic flux. The advection and amplification of the magnetic field at a stagnation flow can give rise to large amounts of Joule dissipation over hydrodynamic time scales. These effects may lead to an accelerated annihilation of the magnetic field, or to steady state dissipative layers, depending on the balance between the incoming magnetic flux and the dissipation rate. The basic elements of the flow enhanced dissipation mechanism are discussed using order of magnitude considerations. Analytic time dependent solutions that describe the evolution of the magnetic field are obtained for planar flows. Starting from generic initial and boundary conditions for the magnetic field component lying on the plane of the flow, it is shown that the sublayer in which a change of sign of the magnetic field occurs tends to vanish in a short time during the formation of the current sheet. On the other hand, the magnetic field component normal to the flow plane is always rapidly extinguished. Thus, configurations commonly considered as models for steady state reconnection or tearing instability studies, are exceptional cases rather than generic magnetic structures. Self similar solutions that describe the amplification and decay of the magnetic field for planar and axial-symmetric flows are also obtained. In three dimensional stagnation point flows, current sheets that are not sustained by a continuous injection of magnetic energy are completely annihilated in a few hydrodynamic times. Several applications, including coronal heating, the dayside magnetospheric stagnation point, and the formation of hot spots in the Plasma Focus experiments, are discussed. The influence of stagnation flows on the stability of these dissipative structures is studied. These flows tend to oppose the permanence of a reconnected configuration. Numerical simulations of two-dimensional magnetic reconnection show the build up and consolidation of the current sheet. Thermal effects due to the rise of temperature in the current sheath and the resulting conductivity increment, enhance the amplification and extinction processes. These effects are illustrated with numerical solution examples. The heating and compressibility limits of the model are briefly outlined. Finally, the effect of density variations during the evolution of current sheets in compressible stagnation point flows is also studied numerically.

We study the evolution of solar active regions (ARs) to infer the properties of the flux tubes forming them and to analyze the role that convective and photosferic plasma motions may have in their evolution. We study a set of ARs in which the main polarities are observed to rotate one around the other along several solar rotations. We interpret this peculiar evolution as due to the emergence of distorted magnetic flux tubes. From the observed ARs properties we discuss the possible mechanisms at the origin of the deformation and, after discarding the kink instability and the Coriolis force, we conclude that the most likely mechanism is the interaction of the flux tubes with the convective zone plasma. Next, we analyze the magnetic helicity injection on synthetic magnetic configurations and in an observed AR. We compare this injection to the coronal helicity computed using a linear force free field approximation and to the helicity ejected by coronal mass ejections (CMEs) inferred from magnetic clouds observations. Our results show that the helicity injected by photospheric shearing motions and by the differential rotation are not enough to explain, neither the content of coronal helicity nor the amount of helicity ejected by CMES. Therefore, the main source of coronal magnetic helicity is the twist inherent to the flux tube forming the AR.